Digital Predistortion for Cognitive Radio

ABSTRACT

Embodiments of cognitive radio technology can recover and utilize under-utilized portions of statically-allocated radio-frequency spectrum. A plurality of sensing methods can be employed. Transmission power control can be responsive to adjacent channel measurements. Digital pre-distortion techniques can enhance performance. Embodiments of a high DNR transceiver architecture can be employed.

PRIORITY

This application is related to and claims priority under 35 U.S.C.119(e) to U.S. Provisional Patent Application No. 60/890,801 filed onFeb. 20, 2007 entitled “SYSTEM AND METHOD FOR COGNITIVE RADIO” by HaiyunTang the complete content of which is hereby incorporated by reference.

BACKGROUND

1. Field of the Invention

The inventions herein described relate to systems and methods forcognitive radio.

2. Description of the Related Art

Spectrum Utilization Problems

A recent study by the FCC Spectrum Task Force [United States' FederalCommunications Commission (FCC), “Report of the spectrum efficiencyworking group,” November 2002,http://www.fcc.gov/sptf/files/IPWGFinalReport.pdf] found that while theavailable spectrum becomes increasingly scarce, the assigned spectrum issignificantly underutilized. This imbalance between spectrum scarcityand spectrum underutilization is especially inappropriate in thisInformation Age, when a significant amount of spectrum is needed toprovide ubiquitous wireless broadband connectivity, which isincreasingly becoming an indispensable part of everyday life.

Static spectrum allocation over time can also result in spectrumfragmentation. With lack of an overall plan, spectrum allocations in theUS and other countries over the past several decades can appear to berandom. Despite some efforts to serve best interests at the time, thisleads to significant spectrum fragmentation over time. The problem isexacerbated at a global level due to a lack of coordinated regionalspectrum assignments. In order to operate under such spectrumconditions, a device can benefit from operational flexibility infrequency and/or band shape; such properties can help to maximallyexploit local spectrum availability.

To address the above problems, an improved radio technology is neededthat is capable of dynamically sensing and locating unused spectrumsegments, and, communicating using these spectrum segments whileessentially not causing harmful interference to designated users of thespectrum. Such a radio is generally referred to as a cognitive radio,although strictly speaking, it may perform only spectrum cognitionfunctions and therefore can be a subtype of a broad-sense cognitiveradio [J. M. III, “Cognitive radio for flexible mobile multimediacommunications,” Mobile Networks and Applications, vol. 6, September2001.] that learns and reacts to its operating environment. Key aspectsof a cognitive radio can include:

Sensing: a capability to identify used and/or unused segments ofspectrum.

Flexibility: a capability to change operating frequency and/or bandshape; this can be employed to fit into unused spectrum segments.

Non-interference: a capability to avoid causing harmful interference todesignated users of the spectrum.

Such a cognitive radio technology can improve spectrum efficiency bydynamically exploiting underutilized spectrum, and, can operate at anygeographic region without prior knowledge about local spectrumassignments. It has been an active research area recently.

FCC Spectrum Reform Initiatives

FCC has been at the forefront of promoting new spectrum sharingtechnologies. In April 2002, the FCC issued an amendment to Part 15rules that allows ultra-wideband (UWB) underlay in the existing spectrum[FCC, “FCC first report and order: Revision of part 15 of thecommission's rules regarding ultra-wideband transmission systems,” ETDocket No. 98-153, April 2002]. In June 2002, the FCC established aSpectrum Policy Task Force (SPTF) whose study on the current spectrumusage concluded that “many portions of the radio spectrum are not in usefor significant periods of time, and that spectrum use of these ‘whitespaces’ (both temporal and geographic) can be increased significantly”.SPTF recommended policy changes to facilitate “opportunistic or dynamicuse of existing bands.” In December 2003, FCC issued the notice ofproposed rule making on “Facilitating Opportunities for Flexible,Efficient and Reliable Spectrum Use Employing Cognitive RadioTechnologies” [FCC, “Facilitating opportunities for flexible, efficient,and reliable spectrum use employing cognitive radio technologies,” ETDocket No. 03-108, December 2003] stating that “by initiating thisproceeding, we recognize the importance of new cognitive radiotechnologies, which are likely to become more prevalent over the nextfew years and which hold tremendous promise in helping to facilitatemore effective and efficient access to spectrum.”

While both UWB and cognitive radio are considered as spectrum sharingtechnologies, their approaches to spectrum sharing are substantiallydifferent. UWB is an underlay (below noise floor) spectrum sharingtechnology, while cognitive radio is an overlay (above noise floor) andinterlay (between primary user signals) spectrum sharing technology asshown in FIG. 1. Through sensing combined with operational flexibility,a cognitive radio can identify and make use of spectral “white spaces”between primary user signals. Because a cognitive user signal resides insuch “white spaces”, high signal transmission power can be permitted aslong as signal power leakage into primary user bands does not embodyharmful interference.

Broadcast TV Bands

Exemplary broadcast TV bands are shown in Graph 200 of FIG. 2. Each TVchannel is 6 MHz wide. Between 0 and 800 MHz, there are a total of 67 TVchannels (Channels 2 to 69 excluding Channel 37 which is reserved forradio astronomy). The NPRM [FCC, May 2004, op. cit.] excludes certainchannels for unlicensed use: Channels 2-4, which are used by TVperipheral devices, and Channels 52-69, which are considered for futureauction. Among the channels remaining, Channels 5-6, 7-13, 21-36, and38-51 are available for unlicensed use in all areas. Unlicensed use inChannels 14-20 is allowed only in areas where they are not used bypublic safety agencies [FCC, May 2004, op. cit.].

It can be appreciated that Channels 52-69 are currently used by TVbroadcasters and it is not clear if/when they will be vacated. There issignificant interference in the lower channels 5-6 and 7-13. Based onthese considerations, the spectrum segment 470-806 MHz covering TVchannels 14-69 can be of particular interest.

Spectrum Opportunity in the TV Bands

Spectrum opportunity can be a direct result of incumbent systeminefficiency. In TV bands, a signal from a TV tower can cover an areawith a radius of tens of kilometers. TV receivers can be sensitive tointerference such that TV cell planning may be very conservative toensure there is essentially no co-channel interference. This can leave asubstantial amount of “white spaces” between co-channel TV cells asillustrated in the Map 300 of FIG. 3. Those “white spaces” canconstitute an opportunistic region for cognitive users on a particularTV channel. Each TV channel may have a differently shaped opportunisticregion. The total spectrum opportunity at any location can comprise thetotal number of opportunistic regions covering the location. Ameasurement in one locality shows an average spectrum opportunity in TVchannels 14-69 of about 28 channels; that can be expressed as anequivalent bandwidth of approximately 170 MHz.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 Graph of spectrum sharing technologies: UWB and cognitive radio.

FIG. 2 Graph of exemplary television channel bands.

FIG. 3 Map of television co-channel coverage areas and opportunisticregion.

FIG. 4 Diagram of a cognitive radio system.

FIG. 5 Graph of a DTV transmission mask.

FIG. 6 Graph of simulated non-linearities.

FIG. 7 Diagram of an adjacent channel interference situation.

FIG. 8 Diagram of an adjacent channel measurement based adaptivetransmission power control system.

DETAILED DESCRIPTION

FIG. 4 depicts an embodiment of a cognitive radio system in blockdiagram. A transceiver 401 can be coupled with and/or in communicationwith one or more antennae 402. Baseband signal processing can beprovided by elements of a baseband processor 403. Elements of a basebandprocessor 403 can comprise a sensing processor 404, a transmit powercontrol element 405, and a pre-distortion element 406. In someembodiments a pre-distortion element 406 can be coupled with and/or incommunication with a transceiver 401. In some embodiments a transmitpower control element can be coupled with and/or in communication with atransceiver 401. In some embodiments a collective sensing element 407can be coupled with and/or in communication with a baseband processor403 and/or elements comprising a baseband processor.

In some embodiments transceiver 401 can comprise transceiver and/ortransmitter and/or receiver mechanisms disclosed herein. In someembodiments sensing element 404 can comprise one or more sensingmechanisms as described herein. By way of example and not limitationthese sensing mechanisms can include energy sensing, NTSC signalsensing, and/or ATSC signal sensing. In some embodiments a collectivesensing element 407 can provide collective sensing mechanisms asdescribed herein.

In some embodiments transmit power control 405 can support adaptivetransmit power control mechanisms described herein. In some embodimentspre-distortion element 406 can provide digital pre-distortion mechanismsas described herein.

In some embodiments baseband processor 403 can support additionalprocessing mechanisms as described herein. By way of example and notlimitation these mechanisms can include filtering and/or reconstruction.

Adaptive Transmission Power Control:

In some embodiments, a cognitive user device (cognitive user) cantransmit on a channel after determining that channel to be vacantthrough sensing. The TV-band NPRM [FCC, May 2004, op. cit.] allows amaximum transmission power of 30 dBm (1 W). However, because oftransmitter windowing and nonlinearity, a portion of cognitive usertransmission power can leak into the adjacent channels and can createadjacent channel interference. Adjacent channel interference can bemaintained below a specified level in order to guarantee performance inadjacent channels. Maximum transmission power from a cognitive user canbe limited by such an adjacent channel interference requirement.Adaptive transmission power control can be performed by a cognitive userin order to optimize and/or maximize transmission potential for aspecified channel while causing essentially no harm to operational useof adjacent channels.

Adjacent Channel Interference Requirement:

The FCC may adopt the DTV transmit mask as shown in the graph 500 ofFIG. 5 for a TV-band cognitive radio. This can define exemplaryconstraints for a cognitive radio transmitter, notably regardinginterference with adjacent channels.

Graph 600 of FIG. 6 illustrates simulations of signal power spectra forembodiments of a transmitter with specified nonlinearities. Thesespectra illustrate exemplary leakage behavior in some transmitterembodiments.

Given a specified inband signal transmission power P_(TX), an amount ofadjacent channel leakage (ACL) can be expressed in decibel (dB) unitsas:

P _(ACL) =P _(TX) −R _(ACL)  (1)

where R_(ACL) 701 is a ratio between inband signal power and out-of-bandleakage power due to a combined effect of windowing and nonlinearity, asdiscussed herein with regards to non-linearity analysis and simulation.In practice, leakage can typically be dominated by transmitternonlinearity as shown in FIG. 6 such that (in dB units):

R_(ACL)=2D  (2)

where D is the IP3 (third-order intercept point) clearance of Equation(19) discussed herein. In some embodiments, a digital pre-distortiontechnique can further reduce the above leakage. In some embodiments adigital predistortion technique can further reduce the above leakage byapproximately 20 dB.

The graph 700 of FIG. 7 illustrates an adjacent channel interferencesituation wherein a signal transmission on a cognitive user channel 702can cause interference to one or more adjacent TV channels 703 704. Amaximum tolerable interference on a TV channel can be specified by adesired-to-undesired ratio (DU ratio), R_(DU) 705. In some embodiments,R_(DU) 705 can have a typical value of approximately 30 dB. A maximumallowable interference power P_(ACL) 706 at any TV receiver can beexpressed as a received TV signal power P_(TV) minus a DU ratio in dBunits, i.e.

A _(ACL) =P _(TV) −R _(DU)  (3)

In order to set an interference-free condition that can be guaranteed onboth adjacent TV channels,

P_(TV)=min{P_(TVL),P_(TVR)}  (4)

where P_(TVL) 708 and P_(TVR) 710 are received signal powers on left andright adjacent TV channels, respectively.

Combining equations (1) and (3), a cognitive user transmission powerrequirement P_(TX) 712 can be obtained (in dB):

P _(TX) =P _(TV) −R _(DU) +R _(ACL)  (5)

Equation (5) expresses a cognitive user transmission power requirementfor a TV receiver disposed at essentially the same location as acognitive transmitter. However, in some embodiments, each cognitivetransmitter can have a specified clearance region within whichinterference can be ignored. In the TV-band NPRM [FCC, May 2004. op.cit.], a radius of such a clearance region is specified as 10 meters. Aworst-case interference can occur at an edge of a clearance region.Signal power loss K (r₀) from a transmitter to an edge of the clearanceregion can be derived from the Friis free-space equation [T. S.Rappaport, op. cit.]. Thus a cognitive user transmission powerrequirement P (r₀) can be expressed:

P(r ₀)=P _(TV) −R _(DU) +R _(ACL)

P _(TX) =P _(TV) −R _(DU) +R _(ACL) +K(r ₀)  (6)

In an exemplary embodiment, P_(TV)=−60 dBm, R_(DU)=30 dB, R_(ACL)=60 dB,and K(r₀)=48 dB, so a maximum allowed cognitive user transmission powercan be:

P _(TX)=−60−30+60+48=18 dBm  (7)

or approximately 60 mW.

Reducing adjacent channel leakage ratio—through windowing and/or digitalpre-distortion techniques—can be key to increasing cognitive usertransmission power allowed. A 10 dB reduction in R_(ACL) can result in atenfold increase in allowed transmission power.

Adaptive Transmission Power Control:

Cognitive user transmission power for a specified channel can bemaximized while causing less than a harmful level of interference inadjacent channels; cognitive user transmission power can be responsiveto received signal powers on adjacent TV channels in accord withEquations (4) and (6).

In some embodiments that employ collective sensing techniques, eachcognitive user can periodically broadcast its sensing results in aspecified manner; such results can comprise per channel SNR estimates.By collecting sensing results, in some embodiments a cognitive user canobtain a consensus estimate of signal power on one or more specifiedchannels. Estimated signal powers on adjacent channels can then be usedto derive a suitable transmission power using Equations (4) and (6). Itcan be appreciated that if one of the adjacent channels is deemedvacant, that vacant channel can be advantageously removed fromconsideration in equation (4). An adjacent channel leakage ratio R_(ACL)in equation (6) can be obtained based on pre-tabulated transmitternonlinearity characteristics and/or through active monitoring of atransmitted signal in an embodiment employing a digital predistortiontechnique.

Diagram 800 of FIG. 8 depicts a system embodiment of adjacent channelmeasurement based adaptive transmission power control. A cognitive radioreceiver RX 806 can receive a broadcast signal from antenna 802 viacoupler 804. The receiver RX 806 can provide processing to a receivedsignal (e.g., a broadcast signal) so as to provide specified bandsand/or channels to a power measurement and control unit PMC 801. PMC 801can comprise power measurement elements 810 812 814 correspondingrespectively to adjacent left channel signal power P_(TVL), adjacentright channel signal power P_(TVR), and adjacent channel leakage ratioR_(ACL). Each of the elements 810 812 814 can operate on a signalreceived from RX 806 to provide a corresponding power measurement;P_(TVL), P_(TVR), and R_(ACL) respectively. PMC 801 can further compriseelements that provide specified parameters: desired-to-undesired ratioR_(DU) and clearance region attenuation K(r₀). A control element 820 canreceive parameters P_(TVL), P_(TVR), R_(ACL), R_(DU), and K(r₀) fromrespectively corresponding elements 810 812 814 816 818 and responsivelyprovide a control signal to cognitive radio transmitter TX 808. Controlelement 820 can process parameters P_(TVL), P_(TVR), R_(ACL), R_(DU),and K(r₀) according to Equation (6) and provide a control signal to TX808 that specifies a power transmission level P_(TX) as specified byEquation (6), given the values of the parameters supplied by elements810 812 814 816 818. Cognitive transmitter TX 808 can be adapted toprovide transmission power P_(TX) for a channel at a level specified bya control signal received from control element 820. It can beappreciated that control element 820 can also provide evaluation ofEquation (4), so as to provide a P_(TV) term to Equation (6) from thecontributing parameters P_(TVL) and P_(TVR). Thus, TX 808 can providecognitive radio transmission of a channel through antenna 802 viacoupler 804 at an advantageous power level P_(TX) specified by controlelement 820 and corresponding to Equation (6). It can be appreciatedthat in some embodiments this system comprises an adaptive system; aprovided power transmission level P_(TX) can change, that is, adapt,over time and in response to variations of specified and/or measuredparameters.

Transmitter Nonlinearity Analysis and Simulation:

Transmitter nonlinearity can be a cause of adjacent channel leakage. Atransmitter nonlinearity can be modeled as:

y(t)=α₀+α₁ x(t)+α₂ x ²(t)+α₃ x ³(t)+ . . .  (8)

For a passband signal with appropriate filtering, a nonlinearity modelcan be approximated as:

y(t)≈α₁ x(t)+α₃ x ³(t)  (9)

and an equivalent baseband representation of a signal that hasexperienced such nonlinearity can be expressed as

$\begin{matrix}{{{y(t)} = {{\alpha_{1}{s(t)}} + {\frac{3\alpha_{3}}{4}{{s(t)}}^{2}{s(t)}}}}{Let}} & (10) \\{{y_{1}(t)} = {s(t)}} & (11) \\{{y_{3}(t)} = {{{s(t)}}^{2}{s(t)}}} & (12)\end{matrix}$

Using a baseband signal expression for s(t), it follows that:

$\begin{matrix}{\begin{matrix}{{Y_{1}(f)} = {\int_{- \infty}^{\infty}{{y_{1}(t)}^{{- {j2\pi}}\; f\; t}{t}}}} \\{= {\sum\limits_{k \in \Omega}{{X(k)}{\int_{- \infty}^{\infty}{{h(t)}^{{j2\pi}\; \frac{k}{T}t}^{{- {j2\pi}}\; f\; t}{t}}}}}} \\{= {\sum\limits_{k \in \Omega}{{X(k)}{H( {f - \frac{k}{T}} )}}}}\end{matrix}{and}} & (13) \\\begin{matrix}{{Y_{3}(f)} = {\int_{- \infty}^{\infty}{{y_{3}(t)}^{{- {j2\pi}}\; f\; t}{t}}}} \\{= {\int_{- \infty}^{\infty}{{s(t)}{s(t)}{s^{*}(t)}^{{- {j2\pi}}\; f\; t}{t}}}} \\{= {\sum\limits_{k,l,{m \in \Omega}}{{X(k)}{X(l)}{X^{*}(m)}{\int_{- \infty}^{\infty}{{g(t)}^{{j2\pi}\frac{k + l - m}{T}t}^{{- {j2\pi}}\; f\; t}{t}}}}}} \\{= {\sum\limits_{k,l,{m \in \Omega}}{{X(k)}{X(l)}{X^{*}(m)}{G( {f - \frac{k + l - m}{T}} )}}}}\end{matrix} & (14)\end{matrix}$

where in the second equality

g(t)=h ³(t)  (15)

whose Fourier transform can be expressed as

G(f)=H(f)

H(f)

H(f)  (16)

Note that the window h(t) is a real function.

A signal spectrum can be expressed

$\begin{matrix}\begin{matrix}{{Y(f)} = {{\alpha_{1}{Y_{1}(f)}} + {\frac{3\alpha_{3}}{4}{Y_{3}(f)}}}} \\{= {{\alpha_{1}{\sum\limits_{k \in \Omega}{{X(k)}{H( {f - \frac{k}{T}} )}}}} + {\frac{3\alpha_{3}}{4}{\sum\limits_{k,l,{m \in \Omega}}{{X(k)}{X(l)}{X^{*}(m)}G}}}}} \\{( {f - \frac{k + l - m}{T}} )}\end{matrix} & (17)\end{matrix}$

and the power spectrum can be expressed

$\begin{matrix}\begin{matrix}{{I(f)} = {E\lbrack {{Y(f)}}^{2} \rbrack}} \\{= {E\lbrack {\{ {{\alpha_{1}{Y_{1}(f)}} + {\frac{3\alpha_{3}}{4}{Y_{3}(f)}}} \} \{ {{\alpha_{1}{Y_{1}^{*}(f)}} + {\frac{3\alpha_{3}}{4}{Y_{3}^{*}(f)}}} \}} \rbrack}} \\{= {{\alpha_{1}^{2}{E\lbrack {{Y_{1}(f)}}^{2} \rbrack}} + {2\alpha_{1}\frac{3\alpha_{3}}{4}{Re}\{ {E\lbrack {{Y_{3}(f)}{Y_{1}^{*}(f)}} \rbrack} \}} +}} \\{{( \frac{3\alpha_{3}}{4} )^{2}{E\lbrack {{Y_{3}(f)}}^{2} \rbrack}}}\end{matrix} & (18)\end{matrix}$

A relationship between device nonlinearity coefficients α₁ and α₃ can beexpressed in terms of a two-tone IP3. Specifically, input power to thetwo-tone test can be P_(In) at a distance D (in dB units) from an IP3point P_(IP3), i.e.

P_(IP3)=Dα₁ ²P_(In)  (19)

it follows that

$\begin{matrix}{\frac{3\alpha_{3}}{4} = {{- \frac{\alpha_{1}^{3}}{P_{{{IP}\; 3}\;}}} = {- \frac{\alpha_{1}}{{DP}_{In}}}}} & (20)\end{matrix}$

where compressive third-order nonlinearity can be assumed with α₃<0. Amulti-carrier (such as OFDM) signal of substantially the same inputpower can be applied to a nonlinear device; the output power spectrumcan be expressed

$\begin{matrix}{{I(f)} = {{\alpha_{1}^{2}{E\lbrack {{Y_{1}(f)}}^{2} \rbrack}} - {2\alpha_{1}^{2}\frac{1}{{DP}_{In}}{Re}\{ {E\lbrack {{Y_{3}(f)}{Y_{1}^{*}(f)}} \rbrack} \}} + {\alpha_{1}^{2}\frac{1}{D^{2}P_{In}^{2}}{E\lbrack {{Y_{3}(f)}}^{2} \rbrack}}}} & (21)\end{matrix}$

where the input power of the multi-carrier signal can be expressed

$\begin{matrix}\begin{matrix}{P_{In} = {E\lbrack {\frac{1}{T_{W}}{\int_{- \infty}^{\infty}{{{y_{1}(t)}}^{2}{t}}}} \rbrack}} \\{= {E\lbrack {\frac{1}{T_{W}}{\int_{- \infty}^{\infty}{{{Y_{1}(f)}}^{2}{f}}}} \rbrack}} \\{= {\frac{1}{T_{W}}{\int_{- \infty}^{\infty}{{E\lbrack {{Y_{1}(f)}}^{2} \rbrack}{f}}}}}\end{matrix} & (22)\end{matrix}$

The graph 600 of FIG. 6 shows simulated multi-carrier signal powerspectrums at different IP3s (or different Ds). Nonlinearity can causespectrum “shoulders” in adjacent bands. A difference (in decibel units,(dB)) between inband signal power and the shoulder can be roughly 2D, orthe system dynamic range P_(DR).

The graph 600 illustrates simulated signal power spectra under varyingdevice nonlinearities in a multi-carrier system with subcarrier spacing100 kHz, β=0.16, number of guard band subcarriers 8 (and number of validdata subcarriers 52). Individual curves 602 604 606 608 are shown forIP3-related distance D values of (respectively) 15 dB, 25 dB, 35 dB, and∞.

In some embodiments with a fixed output power, a higher device IP3 canbe required in order to reduce adjacent channel leakage. In someembodiments, an IP3 requirement can be reduced by applying a digitalpredistortion technique and/or process.

Digital Predistortion:

Diagram 900 depicts an embodiment of a system adapted to provide digitalpredistortion. An RF signal can be coupled with an antenna 902 fortransmission. A signal representative of such a transmitted signal canbe obtained via a coupling device 904; such a representative signal canbe of significantly lower power than the transmitted signal. Arepresentative signal can be down-converted, sampled, and fed back to abaseband distortion estimator where it can be compared with acorresponding source baseband signal in order to estimate distortion. Inthe depicted embodiment 900, down-conversion can be provided by an RFdown-converter 906, sampling and conversion to a digital representationcan be provided by an analog to digital converter ADC 908, and abaseband distortion estimator BDE 910 can provide comparison and/orestimation. Resulting distortion information can be provided to abaseband pre-distortion generator such as BPG 908. BPG 908 canpre-compensate a baseband signal for distortion that the signal can beexpected to experience as it passes through elements of a transmitter RFchain. That is, a signal can be pre-compensated for estimateddistortion. It can be appreciated that an estimated distortion cancomprise contributions from any and/or all nonlinear elements in atransmitter chain. In some typical embodiments a major contribution todistortion can be attributed to a power amplifier such as PA 914depicted in Diagram 900. In some embodiments, a distortion compensationloop such as the system of Diagram 900 can run continuously during asignal transmission process in order to track and/or adapt to anyvariations of transmitter nonlinearity. By way of non-limiting example,in some embodiments a distortion compensation loop—that is, a digitalpredistortion system—can track and/or adapt to a transmitternonlinearity corresponding to variations in temperature.

In some embodiments, a baseband distortion estimator BDE 910 candetermine and/or provide a distortion factor, herein described, to abaseband predistortion generator BPG 912. In some embodiments, abaseband predistortion generator can operate on a baseband signal s(t)to provide a predistorted signal s_(PD)(t), as specified herein, to anRF transmission chain. An RF transmission chain can comprise a digitalto analog converter DAC 914, an RF upconverter 916, and a poweramplifier PA 918, as depicted in Diagram 900. A baseband predistortiongenerator BPG 912 can be adapted to provide a predistorted signals_(PD)(t) responsive to a baseband signal s(t) and a distortion factor,as specified by Equation (30).

In some embodiments, information provided to a baseband predistortiongenerator BPG 912 from a baseband distortion estimator BDE 910 cancomprise any known and/or convenient representation of nonlinearityterms. By way of non-limiting example, such nonlinearity terms cancomprise coefficients of a nonlinearity model such as those of Equation(8).

In a multi-carrier system, after appropriate signal processing, e.g.window truncation and FFT, a frequency-domain signal seen by a basebanddistortion estimator can be expressed

$\begin{matrix}{{\sum\limits_{n \in \Omega}{X(n)}} + {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{\sum\limits_{k,l,{m \in \Omega}}{{X(k)}{X(l)}{X^{*}(m)}}}}} & (23)\end{matrix}$

A signal on a channel nεΩ can be expressed

$\begin{matrix}{{Y(n)} = {{X(n)} + {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{\sum\limits_{{k + l - m} = n}{{X(k)}{X(l)}{X^{*}(m)}}}}}} & (24)\end{matrix}$

and a signal on any channel n∉Ω can be expressed

$\begin{matrix}{{Y(n)} = {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{\sum\limits_{{k + l - m} = n}{{X(k)}{X(l)}{X^{*}(m)}}}}} & (25)\end{matrix}$

A distortion factor

$\begin{matrix}{\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}} & (26)\end{matrix}$

can be estimated using signals on channels of adjacent bands. Sincesignal values X(k)s can be known, it can be possible to compute

$\begin{matrix}{\sum\limits_{{k + l - m} = n}{{X(k)}{X(l)}{X^{*}(m)}}} & (27)\end{matrix}$

and then to estimate a distortion factor as

$\begin{matrix}{\lbrack {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}} \rbrack_{est} = \frac{Y(n)}{\sum\limits_{{k + l - m} = n}{{X(k)}{X(l)}{X^{*}(m)}}}} & (28)\end{matrix}$

However, the complexity of computing an intermodulation product sumΣ_(k+l−m=n)X(k)X(l)X*(m) can discourage such an approach. The case of apreamble for which an intermodulation product sum can be pre-computedcan be an exception.

A low-complexity approach can be to use signal power in order toestimate a distortion factor:

$\begin{matrix}{\lbrack ( {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}} )^{2} \rbrack_{est} = \frac{E\lbrack {{Y(n)}}^{2} \rbrack}{E\lbrack {{\sum\limits_{{k + l - m} = n}{{X(k)}{X(l)}{X^{*}(m)}}}}^{2} \rbrack}} & (29)\end{matrix}$

since E[|Σ_(k+l−m=m)X(k)X(l)X*(m)|²] can be a constant that dependsprimarily on a position of a target channel n relative to a channel setΩ and thus can be pre-computed. In some embodiments, this approach cantake a relatively long time to reach a desired accuracy due to anaveraging operation that can contribute to estimating E[|Y(n)|²].

Once a distortion factor can be obtained, a signal pre-distortionoperation can be carried out as expressed here:

$\begin{matrix}{{s_{PD}(t)} = {{s(t)} - {( {1 + e} )\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}{s(t)}}}} & (30)\end{matrix}$

where s_(PD)(t) can be a pre-distorted signal sent to a RF transmitterchain and |e|<<1 can accounts for estimation error. After passingthrough the transmitter chain, the signal can be expressed:

$\begin{matrix}{{{\alpha_{1}{s_{PD}(t)}} + {\frac{3\alpha_{3}}{4}{{s_{PD}(t)}}^{2}{s_{PD}(t)}}} = {{{{\alpha_{1}\lbrack {{s(t)} - {( {1 + e} )\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}{s(t)}}} \rbrack} + {\frac{3\alpha_{3}}{4}{{{{s(t)}}^{2}\lbrack {1 - {( {1 + e} )\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}}} \rbrack}^{2} \cdot \lbrack {{s(t)} - {( {1 + e} )\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}{s(t)}}} \rbrack}}} \approx {{\alpha_{1}{s(t)}} - {( {1 + e} )\frac{3\alpha_{3}}{4}{{s(t)}}^{2}{s(t)}} + {\frac{3\alpha_{3}}{4}{{s(t)}}^{2}{s(t)}} - {2( {1 + e} )\frac{1}{\alpha_{1}}( \frac{3\alpha_{3}}{4} )^{2}{{s(t)}}^{4}{s(t)}} - {( {1 + e} )\frac{1}{\alpha_{1}}( \frac{3\alpha_{3}}{4} )^{2}{{s(t)}}^{4}{s(t)}}} \approx {{\alpha_{1}{s(t)}} - {e\frac{3\alpha_{3}}{4}{{s(t)}}^{2}{s(t)}} - {3\frac{1}{\alpha_{1}}( \frac{3\alpha_{3}}{4} )^{2}{{s(t)}}^{4}{s(t)}}}} = {\alpha_{1}{s(t)}\{ {1 - \underset{\underset{{Estimation}\mspace{14mu} {error}}{}}{e\; \frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}} - \underset{\underset{{Higher}\text{-}{order}\mspace{14mu} {distortion}}{}}{{3\lbrack {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}} \rbrack}^{2}}} \}}}} & (31)\end{matrix}$

Since without pre-distortion, the signal can be expressed

$\begin{matrix}{\alpha_{1}{{s(t)}\lbrack {1 + {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}}} \rbrack}} & (32)\end{matrix}$

Intermodulation can be assumed to be about 30 dB below signal power,e.g.

$\begin{matrix}{\lbrack {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}} \rbrack^{2} \approx {{- 30}\mspace{14mu} {dB}}} & (33)\end{matrix}$

if the estimation accuracy is about 20 dB, i.e.

10 log₁₀ e ²≈−20 dB  (34)

then an estimation error power can be expressed:

$\begin{matrix}{{\lbrack {e\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}} \rbrack^{2} \approx {{- 20} + ( {- 30} )}} = {{- 50}\mspace{14mu} {dB}}} & (35)\end{matrix}$

A high-order distortion power can be expressed:

$\begin{matrix}{{\{ {3\lbrack {\frac{1}{\alpha_{1}}\frac{3\alpha_{3}}{4}{{s(t)}}^{2}} \rbrack}^{2} \}^{2} \approx {10 + ( {- 60} )}} = {{- 50}\mspace{14mu} {dB}}} & (36)\end{matrix}$

Overall intermodulation power after pre-distortion can then be about −50dB. Intermodulation power can be limited by estimation error and/orhigher-order distortion. In order to reduce intermodulation powerfurther, a 5th-order distortion compensation can be specified, inaddition to specifying a 3rd-order distortion compensation process asdescribed above.

In the foregoing specification, the embodiments have been described withreference to specific elements thereof. It will, however, be evidentthat various modifications and changes may be made thereto withoutdeparting from the broader spirit and scope of the embodiments. Forexample, the reader is to understand that the specific ordering andcombination of process actions shown in the process flow diagramsdescribed herein is merely illustrative, and that using different oradditional process actions, or a different combination or ordering ofprocess actions can be used to enact the embodiments. For example,specific reference to NTSC and/or ATSC and/or DTV embodiments areprovided by way of non-limiting examples. Systems and methods hereindescribed can be applicable to any other known and/or convenientchannel-based communication embodiments; these can comprise singleand/or multiple carriers per channel. The specification and drawingsare, accordingly, to be regarded in an illustrative rather thanrestrictive sense.

1. A method comprising: receiving a signal; modifying said signal; anddetermining a pre-distortion based, at least in part, on said receivedsignal and said modified signal.